You should first look for any of the pieces that are required to be in a specific place and place them. Next check to see if any of the remaining figures have a relationship with the figures already placed. First look at pieces that must be on an end, then analyze the relationship between the two, if any, and try to place with respect to those rules as well. Review the rules of any remaining pieces. Try to fit them in without violating the rules for the existing pieces.

When one piece has two options where they can be placed, you can move it to one of the two places, but keep in mind alternate possibilities. If that becomes too complex, just commit to one of the two, try to finish the puzzle, and if you cannot complete the puzzle, try switching that piece to the other place.

At the same time look at hints which may reduce some of the options. For example, if one hint tells you that there are four monsters on the same floor, then this hint alone helps reduce a lot the options.